Application of Exp-function method to Symmetric Regularized Long Wave (SRLW) equation

In this Letter, the Exp-function method with the aid of Maple is used to obtain generalized soliton solution and periodic solution with some free parameters for the Symmetric Regularized Long Wave (SRLW) equation. Suitable choice of parameters in the generalized solution leads to Darwish's solution [A.A. Darwish, A. Ramady, Chaos Solitons Fractals 33 (4) (2007) 1263]. The result shows that Exp-function method is a powerful mathematical tool for solving nonlinear equations arising in mathematical physics.     

Bifurcations and traveling waves in a delayed partial differential equation

Here cell population dynamics in which there is simultaneous proliferation and maturation is considered. The resulting mathematical model is a nonlinear first-order partial differential equation for the cell density u(t,x) in which there is retardation in both temporal (t) and maturation variables (x), and contains three parameters. The solution behavior depends on the initial function varphi(x) and a three component parameter vector P=(delta,lambda,r). For strictly positive initial functions, varphi(0) greater, similar 0, there are three homogeneous solutions of biological (i.e., non-negative) importance: a trivial solution u(t) identical with 0, a positive stationary solution u(st), and a time periodic solution u(p)(t). For varphi(0)=0 there are a number of different solution types depending on P: the trivial solution u(t), a spatially inhomogeneous stationary solution u(nh)(x), a spatially homogeneous singular solution u(s), a traveling wave solution u(tw)(t,x), slow traveling waves u(stw)(t,x), and slow traveling chaotic waves u(scw)(t,x). The regions of parameter space in which these solutions exist and are locally stable are delineated and studied.     

Effect of ultrasound “Preinsonification” of solutions on the structuring of dried microdrop trails

The effect of ultrasound preinsonification of a solution on the kinetics and end result of the drying (evaporation) of a microdrop of this solution on a substrate was examined. The results of experiments with salt solution (NaCl) of albumin drops and of an alkaline (NaOH) solution drops are presented. It is shown that the morphology of the dried microdrop residual trail of a preinsonified solution differs noticeably compared to the microdrop trail of a solution that has not been insonified. The main reasons for the revealed effects are analyzed.     

On the global geometry of the stephani universe

A preliminary investigation of global properties of the Stephani solution of the Einstein field equations is presented. This solution generalizes those of Friedman-Robertson-Walker (FRW) in such a way that the spatial curvature indexk (a constant in the FRW models) is a function of the time coordinate. The de Sitter solution, which is also a special case of the Stephani solution, is analyzed in the Stephani coordinates to gain insight into the global structure of the manifold and its foliation. The general metric is found to have several properties in common with this example. It has singularities which can be avoided either by matching the solution to an (as yet unknown) empty-space solution or confining the curvature index to be positive at all times.     

Inverse analysis and regularisation in conditional source-term estimation modelling

Conditional Source-term Estimation (CSE) obtains the conditional species mass fractions by inverting a Fredholm integral equation of the first kind. In the present work, a Bayesian framework is used to compare two different regularisation methods: zeroth-order temporal Tikhonov regulatisation and first-order spatial Tikhonov regularisation. The objectives of the current study are: (i) to elucidate the ill-posedness of the inverse problem; (ii) to understand the origin of the perturbations in the data and quantify their magnitude; (iii) to quantify the uncertainty in the solution using different priors; and (iv) to determine the regularisation method best suited to this problem. A singular value decomposition shows that the current inverse problem is ill-posed. Perturbations to the data may be caused by the use of a discrete mixture fraction grid for calculating the mixture fraction PDF. The magnitude of the perturbations is estimated using a box filter and the uncertainty in the solution is determined based on the width of the credible intervals. The width of the credible intervals is significantly reduced with the inclusion of a smoothing prior and the recovered solution is in better agreement with the exact solution. The credible intervals for temporal and spatial smoothing are shown to be similar. Credible intervals for temporal smoothing depend on the solution from the previous time step and a smooth solution is not guaranteed. For spatial smoothing, the credible intervals are not dependent upon a previous solution and better predict characteristics for higher mixture fraction values. These characteristics make spatial smoothing a promising alternative method for recovering a solution from the CSE inversion process.     

Spherical/gyroid phase diagram of the diblock copolymer in the median selective solvent

The effect of the median selective solution on the lamellar, spherical and gyroid structures is studied. The self-consistent field equations of the diblock copolymer solution are solved by using the reciprocal space method. It is shown that the spherical and gyroid phases have the lowest free energy in the certain range of the solution concentration. Furthermore, the phase diagram of the ordered structures in the diblock copolymer solution with the median selective solvent is calculated, which is consistent with the experimental results. Supported by the National Natural Science Foundation of China (Grant Nos. 10834014, 10674173, and 30770517) and the National Basic Research Program of China (Grant No. 2009CB930704)     

7-羟基喹啉在二甲基亚砜中的荧光光谱

7-羟基喹啉(7-HQ)是一种具有激发态质子转移(ESPT)效应的有机分子。它溶于乙醇溶剂中,在紫外光的激励下,将发生ESPT反应,荧光光谱出现2个荧光带。7-HQ溶于二甲基亚砜(DMS)溶剂中,则不能发生ESPT反应,其荧光光谱只出现单一荧光带。但样品被强紫外光照射后,其荧光光谱也出现2个荧光带。文章首次报道了这一现象,并通过对7-HQ的乙醇、二甲基亚砜和二甲基甲酰胺溶液的吸收光谱和荧光光谱的研究,探讨产生这一现象的机理。认为7-HQ溶于DMS中被强紫外光照射后荧光光谱的变化是由于DMS被光解并生成水而使7-HQ发生ESPT反应的结果。     

十二烷基硫酸钠(SDS)增强若丹明6G水溶液激光激发荧光谱研究

报道了若丹明6G水溶液添加不同浓度的表面活性剂十二烷基硫酸钠(SDS)时激光激发染料的变化,发现较低的掺入量导致R6G荧光减弱,适量SDS的加入使荧光增强,在5×10-5 mol·L-1的R6G水溶液中,加入6×10-2 mol·L-1 SDS,荧光增强因子达到3.1。当R6G浓度为1×10-4 mol·L-1时,加入2×10-2 mol·L-1,染料激光阈值显著降低。测量了不同浓度的R6G溶液的吸收光谱及加入不同浓度SDS后的荧光谱,分析了不同SDS加入量下R6G荧光减弱及增强的物理机制。     

On the extended KdV equation with self-consistent sources

The positive extended KdV equation with self-consistent sources (eKdV⁺ ESCSs) is firstly presented and its related linear auxiliary equation is derived. The generalized binary Darboux transformation (DT) is applied to construct some new solutions of the eKdV⁺ ESCSs such as N-soliton solution, N-double pole solution and nonsingular N-positon solution. The properties of these solutions are analyzed. Moreover, the interaction of two solitons is discussed in detail.     

Competitive and synergistic adsorption of binary volatile organic compound mixtures on activated carbon

The adsorption of four substances and their binary mixture is investigated via the terahertz time domain spectroscopy(THz-TDS). The selected unary compound(ethanol, acetone, ethyl acetate, and n-propyl acetate) and binary mixture(solution 1 is composed of ethanol and acetone, and solution 2 is composed of ethyl acetate and n-propyl acetate) exhibit different adsorption behaviors with varied polarities. In comparison with single component, solution 1 shows shorter adsorption equilibrium time, faster adsorption rate, and stronger adsorption capacity, which conform to a synergistic adsorption mechanism, while the competitive behavior is attributed to the slower adsorption in solution 2. In addition, the pseudo-second-order equation with terahertz parameter is used to assess the rate of binary component organics. The present results indicate a further understanding of multicomponent adsorption mechanisms.     

Low-threshold lasing of a Rhodamine dye solution embedded with nanoparticle fractal aggregates

The spectral and temporal emission properties of a Rhodamine (Rh) dye solution embedded with nanoparticle fractal aggregates are studied. An experiment on the pump-power density dependence of Rh emission spectra shows that the lasing threshold of a Rh6G solution embedded with TiO(2) nanoparticle fractal aggregates is significantly reduced compared with that of a neat dye solution. The mechanism of this reduction in lasing threshold is discussed, together with the lasing properties of narrow bandwidth and short duration.     

Probabilistic solution of some multi-degree-of-freedom nonlinear systems under external independent Poisson white noises

This paper studies the stationary probability density function (PDF) of the response of multi-degree-of-freedom nonlinear systems under external independent Poisson white noises. The PDF is governed by the high-dimensional generalized Fokker-Planck-Kolmogorov (FPK) equation. The state-space-split (3S) method is adopted to reduce the high-dimensional generalized FPK equation to a low-dimensional equation. Subsequently, the exponential-polynomial closure (EPC) method is further used to solve the reduced FPK equation for the PDF solution. Two illustrative examples are presented to examine the accuracy of the 3S-EPC solution procedure. One example involves a two-degree-of-freedom coupled nonlinear system. The other example is concerned with a ten-degree-of-freedom system with cubic terms in displacement. A Monte Carlo simulation is also performed for simulating the PDF solution of the response. The comparison with the simulated result shows that the 3S-EPC solution procedure can provide satisfactory PDF solutions. The good agreement is also observed in the tail regions of the PDF solutions.     

Effects of co-solutes on the hydrogen bonding structure and dynamics in aqueous N-methylacetamide solution: a molecular dynamics simulations study

The effects of trimethylamine-N-oxide (TMAO), urea and tetramethyl urea (TMU) on the hydrogen bonding structure and dynamics of aqueous solution of N-methylacetamide (NMA) are investigated by classical molecular dynamics simulations. The modification of the water's hydrogen bonding structure and interactions is calculated in presence of these co-solutes. It is observed that the number of four-hydrogen-bonded water molecules in the solution decreases significantly in the presence of TMAO rather than urea and TMU. The lifetime and structural relaxation time of water–water and NMA–water hydrogen bonds show a strong increase with the addition of TMAO and TMU in the solution, whereas the change is nominal in case of urea solution. It is also found that the translational and rotational dynamics of water and NMA slowdown with increasing the concentration of these osmolytes. The slower dynamics of water and NMA is more pronounced in case of TMAO and TMU solution, as these co-solutes strengthen the average hydrogen bond energies between water–water and NMA–water, whereas urea has a little effect on the hydrogen bonding structure and dynamics of aqueous NMA solution. The calculated self-diffusion coefficient values for water and these co-solutes are in similar pattern with experimental observations.     

Effect of Static Magnetic Field on Photocatalytic Degradation of Methylene Blue over ZnO and TiO2 Powders

Magnetic field effects (MFEs) on photocatalytic degradation of methylene blue (MB) solution over ZnO and TiO₂ powders are investigated under static magnetic field up to 0.7 T with light irradiation by ultraviolet (UV) light emitting diode. The UV–visible-near-infrared spectrometer is used to monitor the MB concentrations. The positive MFE is observed for ZnO, while the negative MFE for TiO₂, and both MFEs are increased with the increase in the magnetic field applied. By increasing the settling time (the time interval between the preparation of MB solution and the powder dispersion into the MB solution), the photodegradation abilities under MFEs are decreased for both the catalysts. The cause of MFE is discussed in terms of dissolved oxygen in the MB solution and magnetic adsorption of the constituent molecules.     

Some insights in the sonochemical preparation of cobalt nano-particles

The preparation of cobalt nano-particles from a solution of Co(CO)₃(NO) in n-decane under ultrasonication with a frequency of 20 kHz yielded cobalt particles of a size of ca. 5 nm. The presence of either silica or oleic acid in the solution reduced the particle size to ca. 3 and 2 nm, respectively. The resulting particle size is independent of the ultrasonication time, initial Co(CO)₃(NO) concentration, ultrasound intensity and solution temperature. It is postulated that bubble collapse generates multiple nucleation sites resulting in the formation of cobalt particles with a rather uniform particle size distribution.     

立方五次方非线性Schrodinger方程的动力学性质研究

采用辛算法数值求解了一维立方五次方非线性Schrödinger方程,研究了不同非线性参数下非线性Schrödinger方程的动力学性质.数值结果表明,随着立方非线性参数的增加,系统经历了拟周期状态、混沌状态和周期状态,且在五次方项的调制下,呼吸子解可以退化为单孤子解. 关键词： 非线性Schrödinger方程 动力学性质 孤子 辛算法     

翠绿亚胺碱的超快光克尔和光致吸收效应

报道了在飞秒染料激光脉冲作用下对翠绿亚胺碱（ＥＢ）的二甲基甲酰胺溶液的瞬态共振光克尔和光致吸收效应的研究．时间分辨的光克尔实验表明，翠绿亚胺碱溶液的光克尔信号仅表现一超快响应的成分，可归结为其基态和由于单光子共振吸收和双光子吸收产生的激发态的各振动能级与转动能级之间的弛豫过程．同时通过拟合计算分别给出了翠绿亚胺碱溶液的弛豫时间和三阶非线性极化率．抽运探测实验结果表明，翠绿亚胺碱分子的超快响应的光致吸收效应，主要来自于导致该分子中苯环结构π—π^*跃迁的双光子吸收的贡献． 关键词：     

Approximate solution of the magneto-hydrodynamic flow over a nonlinear stretching sheet

The approximate solution of the magneto-hydrodynamic (MHD) boundary layer flow over a nonlinear stretching sheet is obtained by combining the Lie symmetry method with the homotopy perturbation method. The approximate solution is tabulated, plotted for the values of various parameters and compared with the known solutions. It is found that the approximate solution agrees very well with the known numerical solutions, showing the reliability and validity of the present work.     

Adaptive regularized filtering for BRDF model inversion and land surface albedo retrieval based on spectrum cutoff technique

A regularized inversion method is presented to invert the bidirectional reflectance distribution function (BRDF) model for albedo calculations. It is known as discrete ill-posed inverse problem. Essential issues that must be considered include solution existence, solution uniqueness, instability of the solution process, and geophysical meanings of solution. In order to robustly estimate BRDF models parameters, a spectrum cutoff technique is employed to suppress spurious oscillations due to poor angular distribution, sparse sample size, or both. We studied difficulties in estimating BRDF parameters and analyzed the cause of the instability in the solution, and then presented a novel algorithm. The proposed RSC (Regularized Spectrum Cutoff) method is based on improving the spectrum of the BRDF kernel matrix and can always find suitable BRDF parameters for sparse satellite observations. The algorithm is compared with the MODIS (Moderate Resolution Imaging Spectroradiometer) full retrieval (FR) algorithm, and it is tested to be suitable for the case of sufficient observations. Numerical experiments with POLDER (Polarization and Directionality of the Earth's Reflectances) BRDF datasets and MODIS images suggest that the developed spectrum cutoff method is adaptive and robust, and it is valuable for retrieving land surface BRDF and albedo.     

Gravity and large black holes in Randall-Sundrum II braneworlds

We show how to construct low energy solutions to the Randall-Sundrum II (RSII) model by using an associated five-dimensional anti-de Sitter space (AdS(5)) and/or four-dimensional conformal field theory (CFT(4)) problem. The RSII solution is given as a perturbation of the AdS(5)-CFT(4) solution, with the perturbation parameter being the radius of curvature of the brane metric compared to the AdS length ?. The brane metric is then a specific perturbation of the AdS(5)-CFT(4) boundary metric. For low curvatures the RSII solution reproduces 4D general relativity on the brane. Recently, AdS(5)-CFT(4) solutions with a 4D Schwarzschild boundary metric were numerically constructed. We modify the boundary conditions to numerically construct large RSII static black holes with radius up to ~20?. For a large radius, the RSII solutions are indeed close to the associated AdS(5)-CFT(4) solution.